2020
DOI: 10.48550/arxiv.2008.09086
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Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes

Abstract: Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above.We prove joint Benjamini-Schramm convergence (both in the annealed and quenched sense) for uniform objects in the four families. Furthermore, we explicitly construct a ne… Show more

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Cited by 2 publications
(2 citation statements)
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“…In the last few years, after tremendous progresses on the enumerative and probabilistic theory of maps [7,2,14,23], the focus has started to shift to planar maps endowed with constrained orientations. Indeed constrained orientations capture a rich variety of models [15,13] with connections to (among other) graph drawing [26,4], pattern-avoiding permutations [3,24,5], Liouville quantum gravity [21], or theoretical physics [22]. From an enumerative perspective, these new families of maps are expected to depart (e.g.…”
Section: Introductionmentioning
confidence: 99%
“…In the last few years, after tremendous progresses on the enumerative and probabilistic theory of maps [7,2,14,23], the focus has started to shift to planar maps endowed with constrained orientations. Indeed constrained orientations capture a rich variety of models [15,13] with connections to (among other) graph drawing [26,4], pattern-avoiding permutations [3,24,5], Liouville quantum gravity [21], or theoretical physics [22]. From an enumerative perspective, these new families of maps are expected to depart (e.g.…”
Section: Introductionmentioning
confidence: 99%
“…The results of [18] hold more generally if the bipolar oriented map consists of faces which all have the same size or are allowed to have varying sizes, as long as the face degree distribution has a sufficiently strong tail. (See also the works [13,5], which prove the joint convergence of the NW, NE, SW, SE trees where the SW and NE trees are defined using the so-called dual orientation. )…”
mentioning
confidence: 99%